Presentation for the paper: Szymon Klarman and Thomas Meyer. Prediction and Explanation over DL-Lite Data Streams. In Proceedings of the 19th International Conference on Logic for Programming, Artificial Intelligence and Reasoning (LPAR-19), 2013.

1. Prediction and Explanation over DL-Lite Data
Streams
Szymon Klarman and Thomas Meyer
Centre for Artificial Intelligence Research,
CSIR Meraka Institute & University of KwaZulu-Natal,
South Africa
December 18, 2013
LPAR-19, Stellenbosch

2. LPAR 2013 Prediction and Explanation over DL-Lite Data Streams
Motivation
• Applications generating and consuming streaming semantic data
are becoming increasingly common. Domains include: scientific,
medical, financial, urban, and others.
• Stream reasoning is a new research area of growing importance
dealing with two kind of challenges:
• technological: how to construct reasoning systems to handle the
volume and velocity of streaming data;
• conceptual: what new forms of reasoning can be used to exploit the
real-time, real-world character of the streaming data, in order to
enhance situation awareness of the information system.
E.D. Valle, S. Ceri, F. van Harmelen, D. Fensel. It’s a streaming world! reasoning upon rapidly
changing information. In: IEEE Intelligent Systems 24(6), 2009.
Szymon Klarman, Thomas Meyer (CAIR, South Africa) 1 / 12

3. LPAR 2013 Prediction and Explanation over DL-Lite Data Streams
Overview
Problem:
Prediction and explanation over DL-Lite data streams:
• prediction: from observed data to unobserved present-future,
• explanation: form observed data to unobserved past-present.
Approach:
• use Temporal Query Language (TQL), where TQL = LTL + CQs,
• abduction over temporal rules in TQL,
• study prediction and explanation from logical/computational
perspective.
Contributions:
• the temporal rule formalism,
• dedicated minimality criteria,
• complexity results for different fragments of the formalism,
ranging from NP- to PSPACE-complete.
Szymon Klarman, Thomas Meyer (CAIR, South Africa) 2 / 12

4. LPAR 2013 Prediction and Explanation over DL-Lite Data Streams
Full story in one slide...
Temporal “past-future” rules:
ψ ⇒ φ
where ψ, φ are formulas in Temporal Query Language.
recorded segment
explanation
ΦΨ
prediction
ΦΨ
data stream
Zω-
ω+
n
n
Szymon Klarman, Thomas Meyer (CAIR, South Africa) 3 / 12

5. LPAR 2013 Prediction and Explanation over DL-Lite Data Streams
Data streams and temporal queries
Z
Data stream:
A data stream under a TBox T is an A-sequence A = (Ai)i∈Z (i.e. a
sequence of ABoxes) consistent with T .
Here we assume that T and Ai-s are all expressed in DL-Lite.
Szymon Klarman, Thomas Meyer (CAIR, South Africa) 4 / 12

6. LPAR 2013 Prediction and Explanation over DL-Lite Data Streams
Data streams and temporal queries
Φ
Z
Data stream:
A data stream under a TBox T is an A-sequence A = (Ai)i∈Z (i.e. a
sequence of ABoxes) consistent with T .
Here we assume that T and Ai-s are all expressed in DL-Lite.
TQL = LTL + CQs:
φ ::= [q] | ¬φ | φ ∧ φ | φUφ | φSφ
T , A, i |= [q] iff T , Ai |= q iff db(Ai) |= qT
where q is a CQ, qT is FO-rewriting of q under T , evaluated over Ai
viewed as a database.
Szymon Klarman, Thomas Meyer (CAIR, South Africa) 4 / 12

7. LPAR 2013 Prediction and Explanation over DL-Lite Data Streams
Temporal rules
ΦΨ
Z
n
Two types of TQL formulas:
• past-present: formulas without the operators of type U,
• future-present: formulas without the operators of type S.
Temporal rules:
A temporal rule in TQL is an expression:
ψ ⇒ φ
where ψ, φ are TQL formulas such that ψ is past-present and φ is
future-present.
D. Gabbay. The declarative past and imperative future: Executable temporal logic for
interactive systems. In: Proc. of TLS, 1987.
Szymon Klarman, Thomas Meyer (CAIR, South Africa) 5 / 12

8. LPAR 2013 Prediction and Explanation over DL-Lite Data Streams
Climate application example
The temporal rule ψ ⇒ φ captures a correlation between several
measurements and weather phenomena w.r.t. temporal and spatial
coordinates, known to be a good drought predictor:
ψ = (¬[∃y.(HeavyRainIn(y) ∧ locIn(y, north))] S [∃y, z.(SST(y, low) ∧ NAO(z, high)])
∧ [locIn(x, northeast)]
φ = U ([DroughtIn(x)] ∧ ([DroughtIn(x)] U [SevereDroughtIn(x)]))
In general:
Such rules can capture typical temporal association rules obtained via
data mining over time series data.
Szymon Klarman, Thomas Meyer (CAIR, South Africa) 6 / 12

9. LPAR 2013 Prediction and Explanation over DL-Lite Data Streams
Prediction and explanation
recorded segment
prediction
ΦΨ
Zω-
ω+
n
Definition (Prediction)
Let ψ ⇒ φ be a temporal rule, where ψ and φ are grounded and
T , Aω, n |= ψ. A prediction at time n from ψ ⇒ φ over T , Aω is an
A-sequence D = (Di)i∈[n,+∞] such that T , Aω D, n |= φ.
Explanation is defined analogically, but in the opposite direction of
temporal rules.
Szymon Klarman, Thomas Meyer (CAIR, South Africa) 7 / 12

10. LPAR 2013 Prediction and Explanation over DL-Lite Data Streams
ABox sequence abduction
solution
Φ
Z
0
Definition (A-sequence abduction)
An A-sequence abduction problem is a tuple (T , A, φ), where T is a TBox,
A = (Ai)i∈[0,k] is an A-sequence, for some k ≥ 0, and φ is a grounded
future-present TQL formula. A solution to (T , A, φ) is an A-sequence
D = (Di)i∈[0,+∞], such that A D is consistent with T , and
T , A D, 0 |= φ.
Szymon Klarman, Thomas Meyer (CAIR, South Africa) 8 / 12

11. LPAR 2013 Prediction and Explanation over DL-Lite Data Streams
ABox sequence abduction
solution
Φ
Z
0
Definition (Minimality criteria)
The solution D is called:
• e-minimal iff for every solution D , if D |= D then D |= D,
• b-minimal iff for every solution D , if T , A D |= D then
T , A D |= D,
• s-minimal iff for every solution D , if D can be homomorphically
mapped on D then D = D .
Szymon Klarman, Thomas Meyer (CAIR, South Africa) 8 / 12

12. LPAR 2013 Prediction and Explanation over DL-Lite Data Streams
Example cntd.
Temporal rule:
(¬[∃y.(HeavyRainIn(y) ∧ locIn(y, north))] S [∃y, z.(SST(y, low) ∧ NAO(z, high)]) ∧
[locIn(x, northeast)] ⇒ U ([DroughtIn(x)] ∧ ([DroughtIn(x)] U [SevereDroughtIn(x)]))
TBox: {HeavyRainIn RainIn, SevereDroughtIn DroughtIn}
Data stream:
. . . −2 −1 0 . . .
locIn(l1, north) locIn(l1, north) locIn(l1, north)
locIn(l2, northeast) locIn(l2, northeast) locIn(l2, northeast)
SST(m1, low) RainIn(l1)
NAO(m2, high)
Predictions:
0 1 2 3 . . .
D1: DroughtIn(l2) SevereDr.In(l2)
D2: RainIn(l1) DroughtIn(l2) SevereDr.In(l2)
D3: SevereDr.In(l2) SevereDr.In(l2)
D4: DroughtIn(l2) DroughtIn(l2) SevereDr.In(l2)
Szymon Klarman, Thomas Meyer (CAIR, South Africa) 9 / 12

13. LPAR 2013 Prediction and Explanation over DL-Lite Data Streams
Complexity results
We cannot compute all infinite predictions! Instead, we can look for
certain finite structures which compactly encode infinite, ultimately
periodic solutions:
D0 D3 D3 D3
ℕ
D1 D2 D4 D2 D4 D2 D4 ...
l
n
0 3 6 91 2 4 5 7 8 10 ...
The complexity ranges as follows:
• TQL: PSPACE-complete,
• TQL∃: DP-complete,
• TQL+, TQL+,∃: NP-complete,
• conjecture: in PTIME for TQL+,∃:
• with uniquely determined temporal ordering of conditions, and
• for b-minimal solutions.
Szymon Klarman, Thomas Meyer (CAIR, South Africa) 10 / 12

14. LPAR 2013 Prediction and Explanation over DL-Lite Data Streams
Conclusions
• the approach allows for studying prediction and explanation from
a purely logical and computational perspective,
• the symbolic layer of temporal rules can usefully mediate between
the semantic and statistical view on data,
• in applications to DL-Lite streams, the method allows for a direct
reuse of existing CQ rewriting/answering techniques and tools.
Szymon Klarman, Thomas Meyer (CAIR, South Africa) 11 / 12

15. LPAR 2013 Prediction and Explanation over DL-Lite Data Streams
Outlook
• replacing the temporal foundation of TQL with some real-time,
probabilistic formalism (better compatibility with causal reasoning
and temporal association rule learning models),
• alternatively, considering a qualitative variant based on defeasible
semantics,
• involving spatial features to facilitate interesting situation
awareness scenarios (e.g., climate change, fire prediction),
• rewriting rule’s trigger into a monitor (more suitable form for
streaming scenarios),
• practical implementations should be feasible using combinations
of executable temporal logic reasoners and temporal relational
databases (SQL:2011).
Szymon Klarman, Thomas Meyer (CAIR, South Africa) 12 / 12